Intrinsically tuned structural panel

ABSTRACT

A structural panel of the skin-stiffener type, commonly used in aircraft construction, having significantly reduced vibration response, noise radiation and increased acoustic fatigue life, has a skin supported by uniformly spaced stiffeners which are located such that the fundamental natural frequencies of stiffener segments are equal to the fundamental natural frequency of skin sub-panels between the stiffener segments. The physical and geometric properties of the skin and stringers and the spacing of the stringers in various disclosed embodiments depend upon the trace velocity of the excitation field, loading conditions to which the panel is subjected, and end-conditions of the sub-panels and stiffeners.

BACKGROUND OF THE INVENTION

This invention relates to a reinforced structural panel, andspecifically, to a skin-stiffener panel having pre-determined vibrationresponse characteristics.

In the past, many attempts have been made to reduce the vibrationresponse of stiffened structures, such as those used in the constructionof aircraft, ships and missiles. Structural panels in aircraft aresubjected to numerous sources of excitation, such as boundary layerturbulence, jet noise, and vibrations transmitted directly fromadjoining structures. Among the undesirable effects of such vibrationare reduced fatigue life of the panel and excessive noise radiation.

In recent years, attention has been focused upon the minimization ofso-called "coincidence peaks" in the vibration amplitude response andradiated noise spectra of aircraft fuselage structures. Thesecoincidence peaks appear in the response spectra when thetrace-velocity, or convection velocity, of a random pressure fieldacting on the panel coincides with the flexural wave speed in the skinat a particular frequency. The trace velocity is that velocity withwhich an incident pressure wave appears to travel along or parallel tothe skin surface. When this condition occurs, the velocity ofpropagation of a particular component of the incident pressure fieldtraveling parallel to the skin surface of the structure coincides withthe flexural wave speed in the skin at a frequency called coincidencefrequency. Two common examples of such a random pressure field to whichaircraft structures are subjected are the high intensity noise emittedfrom the exhaust of a jet engine and the pressure fluctuations in aturbulent boundary layer. When the excitation field and the flexuralwaves are "in phase", large coincidence peaks appear at the coincidencefrequency in the structural response and radiated noise spectra. Noiselevels in the cabin interior and sonic fatigue life of the fuselagedepend upon this coincidence excitation mechanism.

Previous attempts have been made to reduce vibrations of skin panels bythe application of damping tapes directly on the skin. These tapes maybe constrained or unconstrained, and may be applied in single ormultiple layers. Another method of reducing panel vibration involves theuse of rubber wedges or steel shims mounted on the skin near the framesor tear-strips in an aircraft fuselage to help reduce "edge mode"radiation in the skin. A third approach to the problem has involved theplacing of small spring-mass systems on the skin panels midway betweenthe stiffeners so that the spring-mass-skin system acts as a tuneddamper unit. In a variation of this concept, foam rubber materials havebeen used to act as tuned dampers when excited in a thickness-resonancemode.

It has been found that increasing the number of damping tapes on theskin becomes less and less effective when the skin loss factor isincreased beyond a certain level. It is yet to be demonstrated whetheror not rubber wedges or metallic shims placed near the panel boundariesare more effective than damping tapes of equal weight applied over thewhole panel surface. The use of tuned damper units has often resulted inexcessive structural weight, and fatigue failure of the skin panel nearthe location of the tune damper has also been observed.

An object, therefore, of this invention is to provide a novel andimproved structural panel having significantly reduced vibrationresponse and radiated noise using known materials and assemblytechniques without incurring excessive weight penalties.

Another object of this invention is to provide a novel structural panelof general utility having components which are intrinsically tuned toeach other so that vibration response and radiated noise are minimizedand the sonic fatigue life of the panel is significantly increased.

Another object of this invention is to define a novel structural panelin which skin thickness, stiffener cross-section and stiffener spacingare optimized for a given total structural weight so that vibrationresponse and radiated noise are minimized.

BRIEF SUMMARY OF THE INVENTION

This invention provides for a structural panel having a skin which issupported by a uniformly spaced array of stiffeners attached thereto andspaced in such a way that fundamental flexural natural frequency of aportion of the panel bounded by stiffener segments, referred to hereinas a sub-panel, is equal to the fundamental natural frequency ofstiffener segments. According to this invention, the skin and stiffenercomponents of a structural panel are intrinsically tuned to each otherso that radiation of sound waves due to flexural waves in the skin issubstantially reduced or eliminated.

In one embodiment of this invention, skin sub-panels are tuned to matchbending-mode vibrations of adjoining stiffeners, and in anotherembodiment, torsional-mode oscillations of the stiffeners are matched.Another disclosed embodiment includes the use of damping means such asdamping tape to increase the damping loss factor of the stiffeners.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 and 8 each show a section of a typical skin-stiffener panel asused in an aircraft fuselage.

FIG. 2 shows a skin-stiffener model having uniformly spaced stiffeners.

FIG. 3 illustrates the reflection and transmission of flexural waves inthe skin at the point of attachment of a stiffener.

FIG. 4A is a cross-section of a stiffener with contrained dampingtreatment.

FIG. 4B is the cross-section of a boron-epoxy reinforced stiffener.

FIG. 4C is the cross-section of a fiber-reinforced composite stringer.

FIG. 5 illustrates the computed effect of intrinsic structural tuning onthe velocity response at the center of a model structural panel.

FIG. 6 illustrates the computed effect of intrinsic structural tuning onthe skin bending moment or stress response near the stiffener locationin a model structural panel.

FIG. 7 illustrates the use of intrinsic structural tuning to obtainoptimum stringer spacing for which the computed skin panel velocityresponse and stress response are minimum.

DETAILED DESCRIPTION

The skin-stiffener panels commonly found in aircraft fuselages arereinforced by stringers which run longitudinally through the fuselageand frames which run circumferentially about the fuselage.

FIG. 1 shows a section of a typical such panel where the stringers 10are spaced a distance a apart, the frames 12 are spaced a distance bapart, and the skin 14 is riveted to the stringers and frames. In FIG. 8a similar panel section is shown where the frames 13 are not attacheddirectly to the skin 15 and angles 11 of FIG. 1 have been removed.

The aft fuselage section of an aircraft with wing-mounted engines isfrequently subjected to high noise levels from the engines, especiallyduring take-off. This incident jet noise tends to generate complexstructural wave motion in the fuselage skin. Under cruising conditionsin flight, pressure fluctuations over the skin's surface caused byboundary layer turbulance also tend to generate wave motion in thestructure. The resulting structural vibrations cause high noise levelsin the cabin interior and may eventually cause fatigue failures to occurin the skin panels near the stringer attachment points.

The natural frequency of the curved, pressurized skin panels in the aftsection of a typical jet transport with wing-mounted engines has beenfound to be in the neighborhood of 500 Hz to 600 Hz. It has also beenfound that peak interior noise in the aft section of the fuselageresults primarily from jet noise. Further, jet noise has a tracevelocity which is typically much higher than the speed of sound and iscorrelated over a large area. Therefore, it is convenient in analyzingpanel vibrations due to jet noise excitation to represent it as anexcitation field of random pressure fluctuations having infinitely largetrace velocities along the skin with no decay of correlation.

In a typical fuselage skin-stiffener panel, the frames are considerablymore rigid than the stringers. When the skin is directly attached to theframes as well as the stringers, the panels on either side of each frametend to vibrate independently of each other, whereas adjacent panelsbounded between two frames are strongly coupled and tend to vibrate as agroup rather than as isolated panels. A representative structural modelof such a group of circumferentially adjacent panels is shown in FIG. 2.The panel is composed of a skin 16 and a number of parallel, equallyspaced stringers 18 attached to the skin by rivets or other means.Occasionally in this disclosure, that portion of the skin 20 which isbounded by adjacent stiffeners and frames, in this case a rectangularsection having sides of lengths a and b, is referred to as a sub-panel.Also, adjoining sub-panels are occasionally referred to collectively asa panel or a structural panel.

When a flexural or bending wave in the skin meets a discontinuity in thestructure such as a stringer, part of the wave is transmitted to thenext panel, part is absorbed by the stringer in bending and rotation,and the remainder is reflected back into the panel as illustrated inFIG. 3. The amounts of wave energy absorbed and reflected by thestringer depend upon the stiffness of the stringer in bending andtorsion. At the coincidence frequency, F_(c), the waves reflected by anytwo adjacent stringers reinforce each other, and the amplitude ofvibrations in the sub-panel between the two stringers increases to alarge value. For an excitation field having an infinite trace velocity,the coincidence frequency is close to the fundamental flexural naturalfrequency of the sub-panel, assuming it to have clamped edges at thestringers and simply supported edges at the frames. Under this sort ofexcitation, the adjacent panels vibrate in phase and the stringers donot rotate. The wave reflection process is not affected by the stringerrotational stiffness K_(r), but is influenced by the stringer bendingstiffness K_(t). The stringer bending stiffness is related to thematerial and geometric properties of the stringer and its flexuralvibration frequency by the following equation:

    K.sub.t =  EI.sub.b (π/b).sup.4 -  pA (2π f).sup.2   (Equation No. 1)

where:

E = Young's modulus for the stringer material;

p = density of the stringer material;

I_(b) = area moment of the stringer cross-section in bending;

A = stringer cross-sectional area;

b = frame spacing; and

f = frequency of stringer oscillation in bending.

If the stringer is assumed to be simply supported at the frames, itvibrates like a simply supported beam of length b having a fundamentalflexural natural frequency F_(sb) given by the equation: ##EQU1##

From equation (1) it can be seen that if the stringer is vibrating atF_(sb), K_(t) = 0. If both the stringers and the panel are vibrating atthis frequency, the presence of the stringers is not felt by the skinand the panel responds as a continuous, stringerless structure in thecircumferential direction. Under this condition, there is no wavereflection from the stringers, so the skin response reduces to a smallvalue. However, if the stringer natural frequency and the sub-panelnatural frequency differ substantially, the stringers either appear toostiff or too massive to the panel and there is a substantial reflectionat the stringers, resulting in a large response at the panel naturalfrequency.

Therefore, if the dimensions of the stringers and the panel are chosensuch that the fundamental natural frequency of the stringer acting as abeam equals the fundamental flexural natural frequency F_(cs) of thepanel with edges clamped along the stringers and simply supported alongthe frames, the stringers will not offer any impedence to the bendingwaves propagating at F_(cs), and the skin response will reduce to asmall value.

The expression for F_(cs) is known to be: ##EQU2## where: E' = Young'smodulus for the skin material;

p' = density of the skin material;

t = skin thickness;

ν = Poisson's ration for the skin material;

a = frame spacing; and

b = stringer spacing

Thus, by equating F_(sb) from equation (2) to F_(cs) from equation (3 )and rearranging terms into a more convenient form we find that: ##EQU3##

If the skin and stringers are made of the same material, equation (4)simplifies to: ##EQU4##

These two equations relate the essential geometric and materialproperties of a flat, unpressurized skin-stiffener panel that isintrinsically tuned to minimize panel response to a random pressurefield due to jet noise having a very high trace velocity as previouslydiscussed. Groups of panels so constructed can be placed along the aftfuselage of the jet aircraft having wing-mounted engines in order toreduce structural response to the intense noise generated by the enginesduring take-off. Under these conditions the trace velocity of theexcitation field will be quite high and the fuselage skin will not beexposed to significant pressure differentials between the inside andoutside of the fuselage.

Equation No. 1 for K_(t) is based on the assumption that the stringersare simply supported at the frame location. If the stringers are fullyfixed, the proper expression for F_(sb) is: ##EQU5## where R = (1.506)²= 2.268 for the fundamental mode. The tuned skin-stringer panel in thiscase should be designed to satisfy the following equation: ##EQU6##where R is a factor which depends on the stringer end conditions.

In a practical design, the stringers are neither simply-supported norfully fixed at the frames, but the choice of the factor R (where1≦R≦2.268) for any specific structure can be quickly determined by thoseskilled in the art.

In developing the foregoing equations, it has also been assumed that theskin sub-panels are simply-supported at the frames. In practice, theframes may or may not be directly attached to the skin as FIG. 8 shows.Even when the frames are "shear-tied" to the skin, the skin edges on theframes are neither simply-supported no fully fixed. However, for mostpractical constructions with (b/a) equal to or greater than 2, the panelnatural frequencies are influenced very little by the panel boundaryconditions at the frames, and assumption of simply-supported boundaryconditions at the frames should generally give a good estimate of thepanel natural frequency.

In some cases, the trace velocity of the excitation field acting on theskin may be low enough that there is a coincidence excitation of"stringer torsion" mode of the stiffener panel. This type of excitationcan arise from the random pressure field in the turbulent boundary layerflowing over the fuselage of an aircraft flying at a high subsonicspeed. In this situation where the stringer torsion mode of the panel isstrongly excited, the wave form in the skin panels in such that skindeflections at the stringers are negligible and the effect of stringerbending stiffness K_(t) is no longer significant. The skin insteadinduces torsional oscillations in the stringers and the transmission ofthese oscillations across the stringers depends largely on the stringertorsional stiffness, K_(r). The expression for K_(r) is: ##EQU7## where:W = warping constant of the stringer cross-section about the point ofskin contact (shown as point s in FIG. 4);

e = young's modulus of the stringer material;

b = stringer spacing;

G = shear modulus of the stringer material;

C = St. Venant's constant for uniform torsion of the stringer;

I_(s) = the polar moment of the stringer cross-section about point s (asin FIG. 4);

f = frequency of stringer torsional oscillation.

This equation shows that K_(r) is frequency-dependent and equals zerowhen the stringer is oscillating at the frequency: ##EQU8##

In order to "tune" a panel subjected to coincidence excitation at ornear the fundamental stringer torsion mode frequency of the stiffenedpanel, the fundamental flexural natural frequency of the skin panel mustbe made equal to the frequency at which K_(r) equals zero. In thissituation it can be assumed that the skin panel behaves as a panel withall four edges simply supported, so that the expression for itsfundamental flexural natural frequency is: ##EQU9## where: E' = modulusof elasticity of the skin panel material;

p' = density of the skin material;

t = thickness of the skin;

ν = Poisson's ratio of the skin material;

a = stringer spacing;

b = frame spacing.

Then by equating F_(st) from equation (9) to F_(ss) from equation (10),we have an expression which relates the geometric and materialproperties of a flat unpressurized skin-stringer panel which isintrinsically tuned to minimize response to excitation by a randompressure field which tends to excite stringer torsion mode of thestiffened panel.

In some cases, the trace velocity of the excitation field acting on theskin may be such that a panel mode having a frequency higher than thefundamental frequency is strongly excited. In these cases, the stringersshould be tuned to that higher mode panel frequency. Again, in somecases the stringers can be designed to act as tuned wave dampers in anyof their overtone modes, if necessary.

It is inherent in a tuned panel that a higher degree of energy istransferred from the skin to the stringers than in a similar untunedstructure. Accordingly, it is necessary that in most applications ofthis concept some means must be provided for damping stringeroscillations to prevent unnecessary reduction in stringer fatigue life.Four common ways known to those skilled in the art to improve thestringer damping loss factor are illustrated in FIGS. 4A, 4B, 4C, and4D. FIG. 4A illustrates the application of visco-elastic dampingtreatment to stringer flanges. One possible improvement of thistreatment involves the application of constrained or tuned dampingtreatment to the flange. In FIG. 4B, various ways are shown toincorporate boron-epoxy fibers longitudinally within the stringers toincrease damping. FIG. 4C shows typical cross-sections of stringersconstructed entirely of fiber-reinforced composites.

Obtaining best results from a tuned panel requires the application ofoptimum damping treatment to the stringers. With most practicalstructures, this can be achieved with the proper application of dampingtape alone and stringer loss factors between 0.10 and 0.5 should beexpected.

In order to demonstrate the dynamic behavior of a tuned structuralpanel, a computer program was written to compare the response of twoflat, unpressurized panels, one tuned and the other untuned, to a randompressure field having a very high trace velocity. For this analysis anoptimum stringer loss factor of 0.35 was used and it was assumed thatthe skin loss factor was 0.01, which is typical for the skin along. Inthe untuned panel it was assumed that the fundamental flexural naturalfrequency of the stringer was 40% of the flexural fundamental naturalfrequency of the panel. It was further assumed for both panels that thetrace velocity of the excitation field was infinite.

In order to obtain results which would provide a meaningful comparison,the geometry of the untuned panel was used as a basis for the design ofthe tuned panel. The "tuning" of the untuned panel was accomplished byassuming that the skin thickness and the stringer area moment remainedconstant and by reducing the stringer cross-sectional area untilequation (4) was satisfied.

Since the stringer area moment remained constant, the tuned structurehad the same static bending stiffness as the untuned one. The tuningprocess described here would be useful in a case where the criticaldesign condition for the panel involved static bending loads. Of course,the tuning process to be used depends upon the critical design conditionfor the panel, and the proper tuning process for given design conditionshould be obvious to those skilled in the art. The particular responsesof the tuned and untuned panels are shown in FIGS. 5 and 6. FIG. 5illustrates the effect of intrinsic structural tuning on the velocityresponse of the panel at its center. FIG. 6 shows a comparison of themaximum bending moment or stress response in the skin quite close to thestringer location. Both figures show an impressive 29 db reduction inresponse as a result of intrinsic tuning. Also, the tuned stringer wasestimated to weigh only about one-sixth as much as the untuned stringer.

Results of this analysis also show that intrinsic tuning produced areduction in the RMS value of the stress response of the panel skin by afactor of four, both at its center and near the stringer locations. Sucha reduction in stress levels in aluminum alloy panels could yield anincrease in the panel's fatigue life by a factor of one thousand.

In another study, the stringer cross-sectional area, skin thickness, andframe spacing were kept constant and the stringer spacing was varied.The tuning condition was satisfied at a particular stringer spacing.FIG. 7 shows the computed reduction of mean square skin velocityresponse and the skin RMS stress when an optimum stringer spacing wasused.

In addition, due to the substantial reduction in velocity response atthe center of a tuned panel, the tensile load on the rivets or fastenersattaching the panel to the stringers caused by inertial loading of theskin is correspondingly reduced. Thus, in a tuned panel, the totalnumber of rivets can be reduced or smaller rivets can be used whilestill satisfying static requirements.

In the foregoing discussion it is implied that a tuned structural panelaccording to this invention must exactly satisfy the relationshipsgiven. Theoretically, proper structural tuning does demand that theserelationships be satisfied, but in practice a panel may be builtaccording to this invention and yet deviate to some degree from theseexact requirements. In some instances, because of other structuralrequirements, it may be difficult to satisfy the tuned conditionexactly. Nonetheless, this invention is useful in this situation becausea substantial reduction in panel response can be achieved even where thestiffener fundamental natural frequencies are allowed to vary from thepanel fundamental natural frequencies by as much as 20%. Also it hasbeen stated that optimum damping treatment of the stringers isdesirable, but in practice, variations in stiffener damping up toapproximately 50% from optimum can be allowed.

Also it should be noted that the preferred embodiments described hereinare flat rectangular panels not to be subjected to pressurization loads.Normally, however, the fuselage of a modern jet transport aircraft ispressurized, and the skin stringer panels making up the fuselage aresubjected to various combinations of axial, bending and shear loads. Theeffect of pressurization loads on the fundamental flexural naturalfrequency of the skin panels is not insignificant and must be taken intoaccount in designing a tuned panel. If the radius of the curvature ofthe panel is large, the effects of the curvature on its dynamic behaviorcan usually be ignored, whereas if the radius is small, the curvaturemust be taken into account. Ordinarily, the effects of other loads notresulting from pressurization can be ignored in calculating the naturalfrequencies of the panel. The effect of pressurization or any otherin-plane loads on the stringer natural frequency is generallyinsignificant. The various methods of calculating the fundamentalflexural natural frequencies of curved and pressurized panels are wellknown to those skilled in the art.

It is also possible using the teachings of this disclosure to reduce lowfrequency interior noise in an aircraft cabin which is a serious problemin all commercial aircraft. Overall cylindrical modes of vibration ofthe fuselage structure must be considered. Calculation of thefundamental (lowest) natural frequency of the cylindrical shell betweentwo successive frame locations taking into account the effects ofpressurization is well known to those skilled in the art. Then,reduction in this low frequency interior noise and structural vibrationcan be accomplished by tuning the fundamental frequency of thecylindrical shell between two successive frame locations to the flexuralor torsional fundamental frequency of the frame stiffener considered asa ring.

A further application of the teachings of this disclosure is possible inthe construction of an optimum fuselage structural configuration havingmimimum noise radiation and structural response. In this optimumconfiguration, the fundamental frequency of the portion of the stringersin between two successive frames is tuned to the fundamental frequencyof the skin sub-panel bounded by stringers and frames, and also thefundamental frequency of the frame considered as a ring is tuned to thefundamental frequency of the cylindrical skin segment bounded by twosuccessive frames.

This invention can be used in yet another important situation. Rib-skinconstruction consisting of a skin stiffened by a set of uniformly spacedribs is commonly used in the tail plane, control surface and wing box ofan aircraft. In many cases, such structures are subjected to intensebroadband fluctuating random pressure loading. In a design study of sucha structure, the response of a tuned rib-skin structure in which thefundamental frequency of the skin sub-panel bounded by two successiveribs was equal to the fundamental frequency of the ribs, was computed.It was observed that the response of the skin panel attained a minimumvalue when the skin was tuned to the ribs to which an optimum dampingtreatment was applied.

By combining known methods with this disclosure, it is possible to buildintrinsically tuned curved skin stringer panels for use in a pressurizedaircraft structure or a comparable application which is equivalent tothe embodiments shown herein. Accordingly, it will be understood thatobvious changes and modifications to the invention described may be madeby those skilled in the art to which this invention pertains withoutdeparting from the spirit and scope of the invention as set forth in theclaims appended hereto.

What is claimed is:
 1. A structural panel comprising:a skin of uniformthickness, and; an orthogonal network of uniformly spaced stiffenersattached to said skin and dividing said skin into a plurality ofsub-panels, the fundamental flexural natural frequency of a sub-panelvibrating as a diaphragm being substantially equal to the fundamentalnatural frquency of an adjoining stiffener vibrating in bending in aplane normal to the skin.
 2. A structural panel comprising:a skin havinga modulus of elasticity E', a Poisson's ratio ν, a mass density p', anda thickness t; a pair of stiffeners attached to said skin and spacedapart a distance b; a plurality of stiffeners attached to said skin,spaced apart a distance a, each oriented approximately at right anglesto each of said pair of stiffeners, and each having a cross-sectionalarea A, a cross-sectional area moment in bending I_(b), a modulus ofelasticity E, and a mass density p; wherein ##EQU10## and where R is aconstant which ranges in value from 1.000 to 2.268.
 3. A structuralpanel having reduced noise radiation characteristics comprising:a pairof adjacent stiffeners uniformly spaced apart a distance b; a pluralityof stiffeners, each spaced apart a distance a, each attached to andoriented substantially at right angles to each of said pair of adjacentstiffeners, and each having a segment of length b extending between saidpair of adjacent stiffeners and having the same fundamental flexuralnatural frequency F; and, a skin of uniform thickness attached to eachof said pair of said plurality of stiffeners to form a plurality ofsub-panels, each of width a and length b, and each having a fundamentalnatural frequency F, when vibrating as a diaphragm, substantially equalto the fundamental flexural natural frequency F of the said segments ofsaid plurality of stiffeners.
 4. A structural panel having reduced noiseradiation characteristics for use on an aircraft fuselage comprising:twoadjacent frames; a plurality of equally spaced stringers, each attachedto said frames and each having segments of equal length extendingbetween said frames and each segment having the same fundamentalflexural natural frequency F; and, a skin of uniform thickness attachedto said frames and said stringer segments to form a plurality ofsub-panels, each bounded by said frames and a pair of adjacentstringers, and each having a fundamental natural frequency F whenvibrating as a diaphragm substantially equal to the fundamental flexuralnatural frequency F of the stringer segments.
 5. A structural panelhaving reduced noise radiation characteristics for use in an aircraftfuselage structure having stringers and frames comprising incombination:two adjacent frames; a plurality of equally spaced stringersegments, each extending between said attached to said frames, and eachhaving the same fundamental flexural natural frequency F; and, a skin ofuniform thickness extending over and attached to said frames andstringer segments to form a plurality of sub-panels, each bounded bysaid frames and two adjacent stringer segments, and each having afundamental natural frequency F, when vibrating as a diaphragm,substantially equal to the said fundamental natural frequency F of thestringer segments.
 6. A structural panel having reduced noise radiationcharacteristics for use in an aircraft fuselage structure havingstringers and frames comprising in combination:two adjacent frames; aplurality of equally spaced stringer segments, each extending betweenand attached to said frames, and each having the same fundamentalflexural natural frequency F; and, a skin of uniform thickness extendingover and attached to said frames and stiffener segments to form aplurality of sub-panels, each bounded by said frames and two adjacentstiffener segments, and each having a fundamental natural frequency Fwhen vibrating as a diaphragm within 20 percent of the fundamentalflexural natural frequency F of the stiffener segments.
 7. Incombination with an aircraft fuselage of the type having a series ofannular-shaped frames spaced lengthwise along the fuselage, stringersattached to the frames and running lengthwise along the fuselage andskin panels covering the frames and stringers to form the outer surfaceof the fuselage, the improvement which comprises:two adjacent frames; aplurality of equally spaced stringers, each attached to said frames,each having a segment extending between said frames, and each of saidsegments having the same fundamental natural frequency F when vibratingin the bending mode; a skin of uniform thickness attached to each ofsaid frames and stringers to form a plurality of rectangular sub-panels,each having a fundamental natural frequency F, when vibrating as adiaphragm, substantially equal to the fundamental natural frequency F ofthe stringer segments.